Beam-Gas Ionisation Cross Sections at 7.0 TeV

Transcription

1 EUROPEAN LABORATORY FOR PARTICLE PHYSICS CERN - LHC DIVISION LHC-VAC/AGM Vacuum Technical Note January 1996 Beam-Gas Ionisation Cross Sections at 7.0 TeV A.G. Mathewson and S. Zhang

2 2 1. Introduction The quantity of interest in the ion induced pressure instability in proton storage ring vacuum systems [1] is the so-called critical current, 11Ic, which is defined as the product of the ion induced gas desorption yield 11 (molecules /ion) and the beam current I(A). At beam currents greater than the critical current the vacuum is unstable and large pressure increases are produced. In the calculation of the vacuum stability the equation to be solved is s w =tan( wl) = C (1) where and 2L is the distance between pumps (m) 25 is the pumping speed (ls-1) Cis the specific conductance of the vacuum chamber (ls-1m) cr is the ionisation cross section for the gas molecule (m2) e is the electronic charge= (C) The factor 103 comes from the units used. In practice L, S and C are design parameters for a given vacuum system and equation (1) is solved for w and hence the critical current 11Ic. It can be seen that, for a given value of w, the critical current is inversley proportional to the cross section cr thus its value is of prime importance when making estimations of the vacuum stability. In the LHC the nominal energy of the circulating protons is 7.0 TeV, at which energy the ionisation cross sections for the gases commonly found in vacuum systems, H2, CH4, CO and C02, have not been measured. The purpose of this note is to present, for the record, the expressions used to calculate the ionisation cross sections which were used in the analyses of the vacuum stability of the LHC experimental vacuum chambers and warm straight sections [2,3,4]. It has been proposed to measure the presssure in the cold parts of the LHC by using the 7 TeV proton beam to ionise the residual gas and collecting the resulting electrons [5]. Thus a knowledge of the ionisation cross sections at 7 TeV for the above gases and He (in case of leaks) would be an advantage in that absolute pressures in the cold parts could be measured.

3 3 2. Theory In reference [ 6] and in a recent publication [7] the expressions for the ionisation cross section a based on the Bethe theory were presented. In these same publications the relevant references were given and so will not be repeated here. However, in reference [7] only the relative ionisation cross sections were measured due to uncertainties in the calibration of the gas pressure and the sensitivity of the ionisation detector. At energies greater than 100 kev the ionisation cross section a for a gas by a particle of charge Ze is given by: (2) where a is the ionisation cross section for the gas molecule (m2) c is the speed of light= (m s-1) v is the speed of the ionising particle (m s-1) ~=vi c= for 7.0 TeV protons m is the mass of the electron= Q-31 (kg) M2 and C are constants depending on the molecule and the function x is given by: (3) since ~ is -1 this expression is more useful in the following form: x=2ln(y)-~ 2 (4) where y- ~ - ~1-~2 and and y is the ratio of the energy of the proton relative to its rest mass the rest mass of the proton = GeV the rest mass of the electron =5.11 MeV It is interesting that expression (2) depends only on the charge on the ionising particle and is independent of the mass i.e. in the high energy limit > IOOkeV, protons and electrons of the same velocity, ~ (or y), have the same ionising cross section. For example 7.0 TeV protons have the same ionising effect

4 4 as 3.81 GeV electrons. At CERN, 3.81 GeV electrons may be found in the SPS when it is acting as part of the injection chain for LEP. The electrons are injected from the PS at 3.5 GeV into the SPS where they are accelerated to ZO GeV before being injected into LEP. In Table 1 are given the values of p, y and the function x for protons at Z6 GeV and 7.0 TeV. Table 1 E p y x=2 ln(y)-p2 Z6 GeV Z TeV Z Putting in values for the fundamental constants the expression (Z) for cr can be written: It must be noted that the cross sections measured in reference [6] are so-called counting cross sections where the number of ionising events, irrespective of charge state, are counted. The ionisation cross section which takes into account the charge state of the ion is the gross ionisation cross section. The gross ionisation cross section is what would be measured in an ionisation cell in a proton or electron ring where all the charge from the ions produced by the beam traversing the cell is measured. The difference between the two cross sections is insignificant for molecules with few electrons such as Hz but can be appreciable for Ar [8]. Ideally, for the stability calculations the number of ions in each charge state should be known since multiply charged ions have higher energies than singly charged ions and are more efficient at desorbing gas i.e. their ion induced desorption yield 11 is larger. Table2 Gas M2 c Hz He 0.75Z CH4 4.Z co C Z

5 5 The constants M2 and C have been calculated by Rieke and Prepejchal [5] from measurements of counting ionisation cross sections for various gases and these are given in Table 2 for H2, He, CH4, CO and C02. The gross ionisation cross sections for H2 and N2 have been measured in the ISR at a proton energy of 26 GeV [9] and were found to be higher than the values calculated using the above expressions by a factors of 1.17 and 1.43 respectively (Table 3). Table3 Gas Calculated Measured Measured/Calculated cr x 1o-18 cm2 cr x 1o-18 cm2 (26 GeV) (26 GeV) H N To be prudent in our estimations of the vacuum stability we have therefore taken the calculated values of the ionisation cross sections from equation (2) and increased them by a factor of 1.2 for H2 and He and by 1.5 for the heavier molecules CH4, CO and C02 to bring them in line with the values measured at 26 GeV for H2 and N2. In Table 4 are shown the ionisation cross sections for H2, He, CH4, CO and C02 calculated for 26 GeV and 7.0 TeV protons. Also shown are the correction factors applied to the 7.0 TeV values. The corrected ionisation cross sections are those that are used in the calculations of vacuum stability in the LHC at 7.0 TeV. Table4 Gas Calculated Calculated Correction Corrected cr x cm2 cr x 1o-18 cm2 Factor cr x 1o-18 cm2 (26 GeV) (7 TeV) (7 TeV) H He CH co C Conclusions The expressions used to calculate the ionisation cross sections of H2, CH4, CO and C02 for 7.0 TeV protons have been presented.

6 6 At energies greater than 100 kev the ionisation cross section depends only on the speed and charge on the ionising particle and is independent of the mass thus protons and electrons of the same speed have the same ionising effect. The ionisation cross sections for 7 TeV protons may be measured by using 3.81 GeV electrons in the SPS. The calculated cross sections for H2 and N2 were smaller than those measured at 26 GeV at the ISR by factors of 1.17 and 1.43 respectively. Thus the calculated values for H2 were increased by 1.2 and all those for the heavier molecules by a factor of 1.5 and it is these corrected cross sections which are used in the calculations of the vacuum stability in the LHC. 4. Acknowledgements The authors are indebted to Dr. K. Eggert for useful discussion and to Drs. R. Calder and 0. Griibner for a critical reading of the manuscript. References [1] Fischer and Zankel, CERN Divisional Report ISR-VA/73-52, [2] A. G. Mathewson, C. Reymermier and S. Zhang, Vacuum Group Technical Note, AT-VA/AGM 95-21, November (1995). [3] A. G. Mathewson, C. Reymermier and S. Zhang, Vacuum Group Technical Note, AT-VA/ AGM November (1995). [4] A. G. Mathewson and S. Zhang, Vacuum Group Technical Note, AT- V AI AGM 95-23, November (1995). [5] A. Poncet, LHC Note 316, March (1995). [6] F. F. Rieke and W. Prepejchal, Phys. Rev. A6, 1507 (1972). [7] H. Ishimaru, S. Shinkichi and M. Inokuti, Phys. Rev. A, Vol. 51 No. 6, 4631, (1995). [8] M. E. Rudd, R. D. DuBois, L. H. Toburen, C. A. Ratcliffe and T.V. Goffe, Phys. Rev. A28, 3244 (1983). [9] 0. Griibner and P. Strubin, IEEE Trans. on Nucl. Sci., Vol. NS-24, No. 3, p 1376, June (1977).